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Area of Science:

  • Complex networks
  • Network science
  • Statistical physics

Background:

  • Classical network theory posits individuals accumulate in highly connected nodes.
  • Heterogeneous networks often exhibit complex transport dynamics.
  • Understanding individual movement patterns is crucial in various scientific domains.

Purpose of the Study:

  • To model individual transport across heterogeneous scale-free networks.
  • To investigate the influence of weakly connected nodes with heavy-tailed residence times.
  • To challenge the established understanding of node attraction in networks.

Main Methods:

  • Modeling transport on a heterogeneous scale-free network.
  • Applying the empirical law of the axiom of cumulative inertia.
  • Utilizing fractional analysis to study network dynamics.

Main Results:

  • Anomalous cumulative inertia overrides the attraction of highly connected nodes.
  • Individuals are preferentially attracted to weakly connected nodes.
  • A U-shaped residence time distribution was derived and observed empirically.

Conclusions:

  • The study fundamentally challenges the classical accumulation of individuals in high-order nodes.
  • Anomalous cumulative inertia is a key factor in network transport.
  • The derived U-shaped distribution has implications for understanding human mobility and employment patterns.